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This video explains how Shor's Algorithm factors the pseudoprime number 314191 into its prime factors using a quantum computer. The quantum computation relies on the number-theoretic analysis of the factoring problem via modular arithmetic mod N (where N is the number to be factored), and finding the order or period of a random coprime number mod N. The exponential speedup comes in part from the use of the quantum fast fourier transform which achieves interference among frequencies that are not related to the period (period-finding is the goal of the QFT FFT).
REFERENCES
RSA Numbers (sample large numbers to try factoring)
https://en.wikipedia.org/wiki/RSA_num...
IBM on RSA https://www.ibm.com/support/knowledge...
Modulo Multiplication Group Tables http://mathworld.wolfram.com/ModuloMu...
Difference of squares factorization https://en.wikipedia.org/wiki/Differe...
Euclid's Algorithm https://en.wikipedia.org/wiki/Euclide...
Rational sieve for factoring https://en.wikipedia.org/wiki/Rationa...
General Number field Sieve https://en.wikipedia.org/wiki/General...
Scott Aaronson blog post about Shor's Algorithm https://www.scottaaronson.com/blog/?p...
Experimental implementation of Shor's Algorithm (factoring 15, 21, and 35) https://arxiv.org/pdf/1903.00768.pdf
Adiabatic Quantum Computation factoring the number 291311 https://arxiv.org/pdf/1706.08061.pdf
Scott Aaronson course notes https://www.scottaaronson.com/qclec/ https://www.scottaaronson.com/qclec/c...
Shor's Algorithm on Quantiki https://www.quantiki.org/wiki/shors-f...
TLS And SSL use RSA encryption https://en.wikipedia.org/wiki/Transpo...
Dashlane security whitepaper https://www.dashlane.com/download/Das...
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How Shor's Algorithm Factors 314191 ─ minutephysics
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